\newproblem{lay:2_2_19}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 2.2.19}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
  If $A$, $B$ and $C$ are invertible $n\times n$ matrices, does the equation $C^{-1}(A+X)B^{-1}=I_n$ have a solution, $X$?
	If so, find it.
}{
  % Solution
	If $B$ and $C$ are invertible, so are $B^{-1}$ and $C^{-1}$, and their inverses are $B$ and $C$, respectively. In this way,
	we may multiply on the left by $C$ and on the right by $B$ to obtain
	\begin{center}
		$CC^{-1}(A+X)B^{-1}B=CI_nB$ \\
		$A+X=CB$ \\
		$X=CB-A$
	\end{center}
}
\useproblem{lay:2_2_19}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
